The behaviour of the Delta nu =2 CO bands around 2.3 micron was examined by comparing observed and synthetic spectra in stars in globular clusters of different metallicity. Changes in the 12C/13C isotopic ratio and the carbon abundances were investigated in stars from 3500--4900 K in the galactic globular clusters M71, M5, M3 and M13, covering the metallicity range from --0.7 to --1.6. We found relatively low carbon abundances that are not affected by the value of oxygen abundance. For most giants the 12C/13C ratios determined are consistent with the equilibrium value for the CN cycle. This suggests complete mixing on the ascent of the red giant branch, in contrast to the substantially higher values predicted across this range of parameters by the current generation of models. We found some evidence for a larger dispersion of CDC in giants of M71 of metallicity [mu] = [M/H] = -0.7 in comparison with the giants of M3, M5 and M13, which are more metal deficient. Finally, we show evidence for lower 12C/13C in giants of globular clusters with lower metallicities, as predicted by theory.